This study reports experimental test results on a solar-pumped laser that utilizes composite YAG/Ce:Nd:YAG/YAG/rod with a diameter of 3 mm. We measured an output power of 8.5 W with optical-to-optical conversion efficiency of 1.43% in multimode operation when the laser was exposed to an incoming solar power of 593 W at an irradiance of 900 W/m2. The YAG/Ce:Nd:YAG/YAG composite laser rod withstood the severe conditions of solar end-pumping for several hours of testing without any negative effects or degradation of laser output over time. To interpret and comprehensively analyze the experimental results, we developed a simulation model based on our experimental setup and conducted calculations with taking into account thermal population of lower laser levels. Simulation calculations show that a small deviation from a straight line in the experimental input–output dependence is a consequence of the weak influence of thermal population of the lower laser levels. To compare with recent achievements with conventional laser rods of comparable sizes and to formulate some useful recommendations when using composite crystals in future studies, we carried out additional numerical experiments taking into account possible optimizations, which do not affect in any way the thermal load on the front part of the laser rod considered in this experiment. The numerical studies demonstrate that solar-to-laser power conversion efficiency of 4.0% is achievable with a 3 mm laser rod when the solar input power is about 600 W. We also discuss the influence of rod size and thermal effects on conversion efficiency. Based on the findings of this study, we conclude that employing laser media composed of a single or multirod system with a composite structure could potentially offer an optimal solution to the thermal challenges inherent in solar-pumped solid-state lasers.